en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y=tan(3x)csc(3x)

Solution

y = tan (3 x) csc (3 x)

Solution

Period : \frac{2 π}{3}

Domain : \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Range : f (x) < - 1 or f (x) > 1

Intercepts : None

Asymptotes : Vertical x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

Extreme Points : None

+1

Interval Notation

Domain : (\frac{2 π}{3} n, \frac{π}{6} + \frac{2 π}{3} n) \cup (\frac{π}{6} + \frac{2 π}{3} n, \frac{π}{3} + \frac{2 π}{3} n) \cup (\frac{π}{3} + \frac{2 π}{3} n, \frac{π}{2} + \frac{2 π}{3} n) \cup (\frac{π}{2} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

Range : (- \infty, - 1) \cup (1, \infty)

Solution steps

Periodicity of

tan (3 x) csc (3 x) : \frac{2 π}{3}

Domain of

tan (3 x) csc (3 x) : \frac{2 π}{3} n < x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Range of

tan (3 x) csc (3 x) : f (x) < - 1 or f (x) > 1

Axis interception points of

tan (3 x) csc (3 x) :

None

Asymptotes of

tan (3 x) csc (3 x) :

Vertical

: x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

Extreme Points of

tan (3 x) csc (3 x) :

None

Popular Examples

f(x)=ln(x^2+x-6)

f (x) = ln (x^{2} + x - 6)

f (x) = (x - 6)^{3}

p(t)=-log_{10}(t)

p (t) = - lo g_{10} (t)

f(x)=x^4+8x^3-9x+9

f (x) = x^{4} + 8 x^{3} - 9 x + 9

f(x)=cos(sqrt(1-x^2))

f (x) = cos (1 - x^{2})

Frequently Asked Questions (FAQ)

What is the y=tan(3x)csc(3x) ?
The y=tan(3x)csc(3x) is